The minimum wiener connector problem
N Ruchansky, F Bonchi, D García-Soriano… - Proceedings of the …, 2015 - dl.acm.org
Proceedings of the 2015 ACM SIGMOD International Conference on Management of …, 2015•dl.acm.org
The Wiener index of a graph is the sum of all pairwise shortest-path distances between its
vertices. In this paper we study the novel problem of finding a minimum Wiener connector:
given a connected graph G=(V, E) and a set Q⊆ V of query vertices, find a subgraph of G
that connects all query vertices and has minimum Wiener index. We show that MIN WIENER
CONNECTOR admits a polynomial-time (albeit impractical) exact algorithm for the special
case where the number of query vertices is bounded. We show that in general the problem …
vertices. In this paper we study the novel problem of finding a minimum Wiener connector:
given a connected graph G=(V, E) and a set Q⊆ V of query vertices, find a subgraph of G
that connects all query vertices and has minimum Wiener index. We show that MIN WIENER
CONNECTOR admits a polynomial-time (albeit impractical) exact algorithm for the special
case where the number of query vertices is bounded. We show that in general the problem …
The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph G=(V,E) and a set Q ⊆ V of query vertices, find a subgraph of G that connects all query vertices and has minimum Wiener index.
We show that MIN WIENER CONNECTOR admits a polynomial-time (albeit impractical) exact algorithm for the special case where the number of query vertices is bounded. We show that in general the problem is NP-hard, and has no PTAS unless P = NP. Our main contribution is a constant-factor approximation algorithm running in time Õ(|Q||E|).
A thorough experimentation on a large variety of real-world graphs confirms that our method returns smaller and denser solutions than other methods, and does so by adding to the query set Q a small number of ``important'' vertices (i.e., vertices with high centrality).
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